Creating value weighted portfolio returns. How to handle missing data?

Question

I am creating portfolios using stock data.

I have some missing data for certain months.

What is the best way to handle this? Should I treat missing months as a return of zero?

I want to try and replicate Kenneth Frenches data, so if anyone had any insight into how that it dealt with in creating his portfolios would be useful.

To give an example,

WSay I've got two stocks, A and B, both starting with a weight of 50%, in month 1, the return of A is 10% and the Return of B is -10%, in the next month the weights 55% and 45% for A and B respectively, however, the return of A is 10% and the return of B is missing. So in month two will, I display the return of my portfolio as 10% or 5.5%, or something else?

Answer 1

Fama and French (1992) state that they "calculate each portfolio's monthly equal-weighted return for July of year $t$ to June of year $t+1$" (see, e.g. Table IV). In that case, it would appear that the results should be fairly insensitive to missing returns, since one would just calculate the average of all of the non-missing stocks.

I would say that your hypothetical scenario of just two stocks in the portfolio is slightly misleading because the portfolio returns would be highly dependent on a single missing stock. Fama and French are looking for systematic factors, and using 1 or 2 stocks to represent a systematic factor would not seem to be very sensible. Given that, I would test to see whether there are more than a handful of stocks in any particular portfolio.

This approach effectively substitutes the missing return with the average return of all the other stocks for the period. This may be a bad assumption if a security has gone bankrupt, but is probably pretty reasonable otherwise. There is an extended discussion of how to deal with missing returns at How to deal with missing returns when creating value (equal) weighted returns